The relationship between family socioeconomic status and the young children’s number sense development: The mediating role of parent-child activities

This study examines the relationship between family socioeconomic status, parent-child activities, and young children’s digital development. Using the Family SES questionnaire, the parent-child activities questionnaire, and the 5 to 6 year old children’s number sense development scale as research instruments, 314 young children (M = 70.42, SD = 3.47). The results show that: (1) Family Socioeconomic Status can significantly positively predict the young children’s number sense development; (2) Parent-child activities play a partial mediating role in the relationship between family socioeconomic status and the young children’s number sense development. This study provides specific guidelines and recommendations for improving the young children’s number sense development.


Introduction
Number sense refers to the understanding of counting, numbers, calculations, and digital systems and structures [1].It is considered as one of the basic mathematical literacies of human beings and the basis for establishing a clear concept of numbers, effectively carrying out mathematical activities such as calculation, and linking mathematics with practical problems [2].Number sense plays an important role in people's understanding of more complex algorithms and in gaining mathematical experience and skills [3,4].
Studies have found that the number sense performance in young children's kindergarten is significantly related to their math scores at the end of the third grade, and it is a strong predictor of math scores in primary school.Furthermore, the development level of number sense in early childhood can effectively predict the performance of standardized math tests after young children enter school and be a powerful predictor of young children's future math difficulties [5,6].Therefore, it is of great practical significance to study the influencing factors and mechanism of young children's number sense ability.This will aid in formulating strategies to cultivate young children's number sense development and lay a foundation for their future mathematical development.
Research shows that the socioeconomic status (SES) of a family is an important variable that affects children's academic achievement [7,8].Foreign studies indicate that children from low SES families are at a disadvantage in number sense performance compared to their peers with middle and high SES.They are also more likely to become a high-risk group for math difficulties in the future [9][10][11].The development of children with low SES in counting, number relations, and number operations is delayed [12].This difference has been observed before children enter kindergarten and persists even after kindergarten education, becoming even more pronounced [13].After formal schooling, these low SES children continue to face serious academic problems in math [14,15].It is evident that family SES is an important variable that influences young children's number sense development.
However, compared to the close attention paid by foreign countries to the relationship between SES and children's number sense development, domestic research on the number sense development started late.Currently, the primary focus of domestic research is on school-age children, with research content primarily concentrating on the correlation between SES and the mathematics academic performance of school-age children [16,17].Little attention has been given to preschool children's number sense development, and there is limited research on the correlation between SES and the young children's number sense development, necessitating Chinese-based data to complement existing research in China.
Therefore, based on previous studies, this research will investigate the relationship between SES and the young children's number sense development in China, and delve deeply into the mechanism through which family SES affects children's number sense development.Additionally, this study assumes that family SES can significantly and positively predict the development level of children's number sense (H1).
The study also points out that the SES of a family, as a background feature of a class group, has a wide influence on the family dynamic process and individual behavior [18,19].The SES of the family not only affects the individual development results but also affects the role of parents in the development of their children.Vygotsky pointed out that parent-child interaction experience is an important mechanism for children's cognitive development [20,21].Family investment theory also suggests that effective interaction between parents and children is often more conducive to children's cognitive development than the provision of family material resources [22,23].
Therefore, in recent years, researchers have paid increasing attention to the influence of family parent-child activities on young children's number sense development.Previous studies have shown that parent-child mathematical activities can impact the development of children's mathematical abilities [24][25][26].Good math parent-child activities can effectively promote the young children's number sense development [27,28].
However, previous studies have only examined the relationship between singular mathematics-related parent-child activities and number sense development.In reality, parent-child interaction within families is varied and comprehensive, encompassing various aspects, rather than solely focused on mathematical experiences.Furthermore, children's early number sense development is influenced by numerous factors.Research on children's early experiences in digital cognitive development and language development demonstrates that language factors play a crucial role in shaping digital concepts [29].The lack of language comprehension may impede problem-solving and affect the expression of mathematical concepts and understanding computational concepts [30,31].Research has shown that quantitative and spatial abilities (e.g., building blocks, picture completion) are positively correlated [32][33][34].Based on this, it can be inferred that in addition to math parent-child activities, children's experiences gained from other parent-child activities, such as language experience from parent-child reading and spatial ability from parent-child building block activities, will also affect young children's number sense development.
The family stress model suggests that when family economic stress is high, family distress will distract parents' attention, and parents with low SES will show less emotional and behavioral concern for their children, resulting in fewer good parent-child interactions [35,36].On the other hand, parents of families with higher SES have a better economic base and more knowledge and time to organize various kinds of parent-child activities that are conducive to children's physical and mental development.Additionally, parent-child activities are better in terms of content, frequency, and quality than those of families with lower SES.From this, it can be speculated that families with low SES have fewer parent-child activities that can promote the young children's number sense development, thus affecting the young children's number sense development.That is, SES may affect the young children's number sense development through the intermediary of parent-child activities.Based on the above, we propose the hypothesis that parent-child activities play a mediating role between SES and the young children's number sense development (H2).The model is shown in Fig 1 .To summarize, this study focuses on preschool children and discusses the relationship among socioeconomic status (SES), parent-child activities, and the young children's number sense development.To address this issue, we collected data from hundreds of families and children, and explored the relationships between variables by establishing structural equation models.This mediation model helps us understand the link between SES and young children's number sense development, the mechanisms by which it occurs, and provides theoretical support for interventions to improve the quality of parent-child activities and young children's number sense development.

Research subjects
The study was approved by the Research Ethics Committee of the Ningde Normal University.During the period from February 2022 to June 2022, 314 young children were randomly selected as subjects from kindergartens in Fujian Province using a convenience sampling method.The kindergarten head explained the purpose and content of the study to the parents and read the informed consent form to them.Full-time kindergarten teachers, who were trained by the researchers, conducted one-on-one tests on the young children, and questionnaires were distributed to the parents of the participating young children.During the test, the teachers emphasized the principle of confidentiality to both the young children and parents, and explained that they could withdraw from the test at any time.The entire data collection process is anonymous.Finally, a total of 296 responses were collected, and 226 responses were valid, accounting for 76.35%.Among them, 109 were boys, accounting for 48.2%, and 117 were girls, accounting for 51.8%.The young children had an average monthly age of 70.42 ± 3.47.

Research tools
Family SES questionnaire.A self-made questionnaire on family economic and social status was utilized, which consisted of five questions.These were: (1) What is your family's monthly income?(2) What is the educational background of the father?(3) What is the educational background of the mother?(4) What is the father's occupation?(5) What is the mother's occupation?The questionnaire utilized a Likert 5-point scoring system, whereby a higher score indicated a higher social and economic status for the family.In this study, the α coefficient of the questionnaire was 0.86.
Parent-child activities questionnaire.A self-made parent-child activities questionnaire was used in this study.The questionnaire consisted of four questions, namely: (1) Do you or your family tell stories or read together with your children at home? (2) Do you or your family often take your children to the library to borrow or read books?(3) Do you or your family play math games, such as counting, addition, and subtraction, with your children at home? (4) Do you or your family play educational games, such as building blocks, puzzles, chess, and cards, with your children at home?The questionnaire utilized Likert's 3-point scoring system, with 1 representing "never" and 3 representing "often."A higher score indicates greater involvement in parent-child activities.In this study, the α coefficient of the questionnaire was 0.72.

5~6-year-old children's number sense development scale
The 5~6-year-old children's number sense development scale, compiled by Jiang [37], has been adopted.The scale comprises five dimensions: counting, number knowledge, number conversion, number grouping, and quantity estimation, with a total of 34 questions.It has been found to have good reliability and validity.The scale is scored on a binary scale, with 1 representing a correct answer and 0 representing an incorrect answer.The higher the score, the more developed the child's number sense.In this study, the α coefficient of each dimension of the scale ranges from 0.66 to 0.81, and the α coefficient of the scale as a whole is 0.89.

Statistical analysis
The study employed SPSS20 for descriptive and correlation analyses of the variables.In addition, Mplus7.4 was utilized to test the mediation model of parent-child activities between family SES and young children's number sense developmental level.The MLR method was applied for parameter estimation, and the mediation effect was assessed using bias-corrected nonparametric percentile Bootstrap.This method can accurately estimate confidence intervals for the mediation effect of the product of regression coefficients and is suitable for non-normal data.Significance of the mediation effect was determined if the obtained effect value's 95% confidence interval did not contain zero [38].

Test for common method bias
To examine whether a significant common method bias existed in this study, an unrotated exploratory factor analysis was conducted on all variables.The results revealed three factors with characteristic roots greater than one.However, the variance explained by the first factor was only 29.58%, which is lower than the critical value of 40% [39].Thus, the findings suggest that there was no significant common method bias in this study.

Descriptive statistics for each variable
In order to test for a close relationship between variables and prepare for the establishment of a structural equation model, Pearson correlation analysis was used to analyze the relationship between variables.The results of the Pearson correlation analysis are shown in Table 1.
Table 1 reveals that gender has a significant positive correlation with parent-child activities but has no significant correlation with family SES and the development level of number sense.The kindergarten level is positively correlated with the development level of number sense, but has no significant correlation with family SES and parent-child activities.
The main variables show a significant positive correlation.The Pearson correlation results indicate that the main variables are closely related, and thus, a structural equation model can be established for further analysis.Moreover, because gender and kindergarten level are significantly related to the research variables, they will be included as control variables in the model.

Mediating role of parent-child activities
In order to test the hypotheses proposed in this study, structural equation models were developed to examine the mediating role of parent-child activities between young children's family SES and levels of number sense, using each questionnaire topic/dimension as an observational indicator.
Firstly, the predictive effect of family SES on the level of number sense was tested.The results indicated that the overall model was well-fitted: χ 2 /df = 2.05, RMSEA = 0.07, CFI = 0.94, TLI = 0.93, SRMR = 0.06.Fig 2 displays the direct effect model, and it demonstrates that family SES significantly and positively predicts the level of number sense (β = 0.27, p < 0.01), thus validating H1.This finding suggests a strong association between the two variables.This shows that there is a close relationship between the two, and intermediary variables can be added to further analyze the influence mechanism of family SES on the level of young children's number sense.
Secondly, the study tested the mediating role of parent-child activities in the relationship between family SES and number sense in young children.The results indicated that the overall model fit well with χ 2 /df = 1.79,RMSEA = 0.06, CFI = 0.93, TLI = 0.91, SRMR = 0.06, and the mediation model is presented in Fig 3 .The findings revealed that family SES significantly and positively predicted parent-child activity (β = 0.48, p < 0.001), and that parent-child activity significantly and positively predicted the level of numerical sense (β = 0.27, p < 0.01).Finally, we tested the mediating effect of parent-child activities on the relationship between family SES and number sense by using bias-corrected nonparametric percentile bootstrap method with 5000 repeated samples.The results are presented in Table 2.The table shows that the mediating effect of parent-child activities between family SES and young children's number sense is significant.The mediating effect value is 0.13, p < 0.01, 95%CI = [0.05,0.25], and the mediating effect accounts for 48.52%, confirming hypothesis H2.

Discussion
Based on previous studies and the family stress model, this study constructs a mediation model to explore the relationship and the mechanism of influence between family SES and the

Family SES can predict the young children's number sense development
This study found that family SES had a significant predictive effect on young children's number sense development, and after controlling for gender and kindergarten level.Young children's number sense development is better in families with high SES.This result is consistent with previous studies [11,15].
Compared with young children from lower family SES backgrounds, those from higher family SES backgrounds may be exposed to higher quality math activities and gain more math learning experience [40].This is because families with high family SES can often provide young children with more educational resources and social support that are conducive to the development of young children.For example, they may play math games with young children more often and provide more opportunities for young children to participate in math thinking development classes.
However, the lack of educational resources and experience in mathematics in families with low family SES can put young children in these families at risk for developmental problems.Their development in counting, number relations, and number operation ability may be delayed before entering school.It is evident that the family's input and support play an important role in the young children's number sense development.

The mediating role of parent-child activities
The results of this study show that parent-child activities play a partially mediating role in the influence of family SES on children's number sense development.Firstly, SES may have a positive impact on parent-child activities, which is consistent with previous research results [41,42], also confirming the views of the family investment model and the family stress model.Compared to parents with low SES, who are forced to focus solely on immediate needs, parents with higher SES will prioritize investing in their children's human capital.They will invest more material and time in their children's early childhood, thereby promoting early development and later educational success.Specifically, families with high SES experience less pressure from economic difficulties and have higher family incomes.Therefore, they have the financial means to enroll their children in higher-quality preschool education programs and more time to engage in parent-child interaction activities.Studies have found that for every 10% increase in family income, parents' investment in early childhood time increases by 0.9 standard deviations [43].At the same time, parents with high socioeconomic status have a higher education level.Parents with a high education level can realize the importance of the early parenting environment for children's development, and these parents are willing to spend more time interacting with children [44, Conversely, lower levels of education may limit parents' awareness of the need to provide a nurturing environment for their children, and therefore, positive parenting activities are less likely to occur.
Secondly, family parent-child activities may positively affect the development level of children's number sense, which is consistent with previous research conclusions [26,46].In parent-child activities, the active interaction between parents and children not only provides children with a rich learning environment with timely feedback but also helps children accumulate mathematical experience and acquire basic mathematical skills such as number recognition and counting.Additionally, this study found that the content related to cultivating reading ability, spatial ability, and gaming ability in parent-child activities is conducive to the young children's number sense development.This finding expands upon previous research.Previous studies have individually confirmed that activities such as parent-child reading and building blocks games each affect the development of children's mathematical abilities [26,46].This study further discovered that various types of colorful daily parent-child activities within the family can collectively contribute to the children's number sense development.
Studies have pointed out that reading skills and mathematics are related [47,48].Having good reading ability can effectively help children understand mathematical story questions [49][50][51].Puzzle games such as building blocks and chess can not only make children gain more cognitive experience in parent-child interaction but also help to improve their thinking logic, thus promoting the young children's number sense development.

Education suggestions
Fully utilize the compensatory function of kindergarten education to mitigate the adverse effects of low SES within families on the young children's number sense development.Young children from low SES families have limited access to educational resources at home, which can limit their learning opportunities.However, improving a family's SES often requires macro-social reform and the long-term efforts of multiple generations, making it a complex and long-term project.However, external forces such as kindergarten education can play a compensatory role, making it more feasible and effective to provide additional resources to support these young children.
On one hand, kindergartens can communicate the importance of parent-child activities to parents through parent-child meetings, demonstrate how to engage in such activities during open days, encourage parents to visit the library with their children, and play games together.Thus guiding parents in conducting meaningful parent-child interactions.On the other hand, kindergarten teachers can establish shared learning spaces and provide more books and learning opportunities for these young children, helping to alleviate the negative impact of their unfavorable family situations.
Parents should engage in diversified parent-child activities as much as possible and fully utilize the role of these activities in promoting the young children's number sense development.According to Bourdieu's theory, the cultural capital owned by families plays a stronger role in class definition and class barriers than economic and social capital [28,52].As an important part of the cultural capital experienced by young children, parent-child activities can effectively promote the young children's number sense development."Life course theory" emphasizes that the younger a child is, the greater the influence of family environmental factors [53].To prevent young children from low SES families from falling behind at the starting point of life due to the lack of family resources, low SES families should pay more attention to the power of parent-child activities and provide more opportunities for young children to engage with diverse learning stimuli through various parent-child activities.This will not only aid in young children's mathematics learning but also compensate for their parents' educational level weaknesses and their own SES in the family, and enhance the young children's number sense development.
Therefore, parents should always accompany their children to engage in some parent-child activities at home, and these activities are not limited to specialized mathematics activities.Reading activities and game activities can also be beneficial.It is not necessary to think that they cannot teach their children mathematics because of their low academic qualifications.Reading with children, taking them to the library, playing with building blocks, and playing chess with them can also contribute to promoting the young children's number sense development.

Research limitations and outlook
There are some limitations to this study: (1) The study only includes research subjects from one province.To increase the ecological validity of the study, future research can include subjects from other provinces; (2) The research design is cross-sectional, which cannot establish a causal relationship among variables.In the future, a longitudinal research design can be adopted to reveal the causal relationship between independent and dependent variables.

Conclusion
In this study, a mediation model was constructed to investigate the relationship between family SES, parent-child activities, and the young children's number sense development.The following conclusions were drawn: (1) family SES can significantly and positively predict the young children's number sense development, and (2) Parent-child activities play an intermediary role in the relationship between family SES and the young children's number sense development.

Fig 2 .Fig 3 .
Fig 2. Direct effect model.Note: The numbers listed in the figure are standardized solutions; The level of the kindergarten is included as a control variable in the model, but is not shown in the figure for the sake of simplicity; ** p < 0.01, *** p < 0.001.https://doi.org/10.1371/journal.pone.0301758.g002